A photonic crystal is generally referred to as to a composite dielectric crystal comprising two or more dielectric materials having different dielectric constants, which are periodically arrayed in such a manner that the crystal has a lattice constant substantially equal to a wave length of light (generally, electromagnetic wave). Light propagating through the photonic crystal has peculiar wave length dispersion characteristics unlike homogeneous dielectric materials.
The photonic crystal may be classified into three kinds of crystal, such as one-, two- and three-dimensional crystals depending upon the number of directions in which the dielectric medium distribution has a periodicity. A variety of structures for respective dimension numbers have been proposed. Several examples are listed in tables of non-patent document 1 described below.
There is disclosed a structure of multi-layered dielectric films having a periodical structure electric thin films which are stacked in an equally spaced manner as one-dimensional photonic crystals. In this structure, the two layers made up of a dielectric thin films having a refractive index higher than 1 and a dielectric layer of the air having a refractive index of 1 (Note that the air layer may be considered as a dielectric layer) are alternately disposed in a periodical manner.
Two-dimensional structure may include a structure in which a dielectric substrate is formed with elongated vertical holes in a square lattice pattern or a triangular lattice pattern, and a structure in which elongated columns are arrayed. Three-dimensional structure may include a structure in which a diamond lattice is implemented by boring a dielectric substrate with three slanted holes which are equally spaced by an angle of 120°. A face-centered cubic lattice structure has been devised in which parallel cross structures comprising dielectric rods which are disposed at an equal space in a parallel manner are stacked in a layered manner.
In such a manner, the photonic crystal can be classified based upon the number of dimensions as well as the periodical structure of the dielectric medium distribution and further classified into triangular lattice, square lattice, diamond lattice, face-centered square lattice structures and the like depending upon its lattice structure. Specific structures are different depending upon the fabrication process of crystals.
Various efforts to implement an optical integrated circuit using such a photonic crystal as a platform have been made since it is considered that use of the photonic band gap of the photonic crystal allows the flow of light in the photonic crystal to be freely controlled.
While, light is generally able to propagate through the photonic crystal, light having a frequency in a specific frequency range is not able to propagate through the photonic crystal. This specific frequency range is referred to as “photonic band gap”. If a defect is introduced into a photonic crystal, the defect provides an inherent mode in which the crystal has an energy level in the photonic band gap. An inherent mode refers a state of electromagnetic field in which the electromagnetic field has a specific energy (equivalent to the frequency) and the distribution pattern of electromagnetic field, and which is independent itself. The inherent mode of the defect may be also simply referred to as “defect mode”. Light in the defect mode in the photonic band gap has an energy in which is concentrated in the vicinity of the defect. Accordingly, light is apparently is confined in the position of the defect.
If the defect which is introduced into the photonic crystal is a point defect, the point defect can be considered as a very small light resonator. If the defect is a line-defect, it can be considered as a light waveguide (optical wiring) since the light is guided along the line-defect.
It is considered that combination of the point defect, line-defect and other defect structure provides various functional elements necessary to form optical circuits, such as power dividers, power combiners, wave length multiplexers, wave length multiplexers, wave length filters, optical switches and the like.
Since even one-dimensional photonic crystal such as a dielectric periodical multi-layered film is able to control transmission of light in one direction, reflection and selection of wave length, it is considered that it is possible to produce simple optical functional elements and one-dimensional circuits for simple optical functional elements. In order to configure complicated optical integrated circuit, it is necessary to two- or three-dimensionally arrange the optical functional elements. Therefore, photonic crystal having a period of two or more dimensions is needed.
Two-dimensional photonic crystal can utilize the properties of the photonic band gap in two directions in which the dielectric constant periodically changes (for example, in x and y directions). Since the distribution of the refractive index is uniform (no changes) in another direction (z direction), light can not be confined by the properties of the photonic band gap. In a practical optical circuit, it is necessary to cause a light beam having a definite diameter input from an optical fiber to propagate in the photonic crystal. However, the light would be dissipated (leaked) in a z direction in which the properties of the photonic band gap can not be used.
On the other hand, since the three-dimensional photonic crystal can utilize the photonic band gap which is common to all three directions, it is considered that it can ideally realize optical guide or other optical functional elements which cause no dissipation (leak) of light. However, the number of steps which are necessary to fabricate the three-dimensional photonic crystal is remarkably larger compared to that of one- or two-dimensional structure, so that it is difficult to fabricate it. Even if it can be fabricated, fabrication cost becomes very high. One of the advantages of integrating the optical circuit resides in a remarkable reduction in fabrication cost. The fact that this advantage can not be obtained is a basic problem of the using three-dimensional photonic crystal as a platform for optical integrated circuit.
Therefore, a structure called as “photonic crystal slab” has been studied to use the photonic crystal for integrated optical circuits. The photonic crystal slab has a structure which is obtained by cutting two-dimensional photonic crystal so that the slab has a definite thickness in a direction (above-mentioned z-direction) in which no changes in the dielectric constant occur.
A detailed structure of the photonic slab is disclosed in patent documents. Drawing of the patent document 1 is cited and is shown in FIG. 15 of the present application. At page 14, column 14 of the patent document 1, there is a description of FIG. 1 (FIG. 15 annexed to the specification of the present application). The substrate 1 is sandwiched on both sides thereof between first and second claddings 2 and 3. The substrate 1 has medium atoms 5 which are periodically buried in a background medium 4 in a two-dimensional and triangular arrangement. Medium atoms which are also termed as atomic dielectric pillars refer to dielectric members which are arranged in a lattice like atoms in a crystalline and whose shape are same as atoms in a crystalline. In this description, “the substrate 1” is equivalent to a structure of the two-dimensional crystal having a definite thickness.
For simplicity of description of the present specification, a layer having a definite thickness equivalent to a portion cut from the two-dimensional photonic crystal in the structure of the photonic crystal slab and dielectric layers which sandwich a core on the both sides thereof will be referred to as “core” and “cladding”, respectively. These technical terms are compliant with those of the slab wave guide.
Confinement of light in a thicknesswise direction in a photonic crystal slab is not achieved using properties of the photonic band gap, but is achieved using total internal reflection properties due to the difference in refractive indices. The confinement will be achieved as follows:
A plane of two-dimensional photonic crystal including two directions in which the dielectric constant changes in a periodical manner is referred to as “periodical plane”. At this time, light which is incident upon the two-dimensional photonic crystal in a direction parallel to the periodical plane will become Bloch wave in which original light (0-order diffracted light) is combined with a number of high order lights at a given ratio. If the cladding is made of such a dielectric material, the wave length of propagating light is longer than that of any diffracted light (including 0-order diffracted light) in the Bloch light, the photonic crystal slab including a core having a definite thickness, which is cut from the two-dimensional photonic crystal is able to confine light in a thicknesswise direction due to total internal reflection effect.
Confinement of light due to total internal reflection in prior art slab wave guide in which the dielectric constant distribution of the core has no periodicity corresponds to a case in the above-mentioned total internal reflection mechanism, in which only 0-order diffracted light exists. In order to confine light in the vicinity of a core layer in the slab wave guide, it is necessary to make the refractive index of the core larger than that of the cladding. In case of the photonic crystal slab, the total internal reflection is achieved by making the transmission refractive index of the core layer regarding an individual diffracted wave larger than that of the cladding.
In such a manner, confinement of light in a thicknesswise direction is achieved by total internal reflection due to difference in refractive index in case of photonic crystal slab. Unlike the case of the photonic band gap, total internal reflection does not necessarily occur in all portions of the photonic crystal slab. If there is a portion in which the periodicity of the refractive index collapses in a light propagating direction in the photonic crystal slab, diffracted light having a wave length larger than that in the cladding layer is generated.
Accordingly, the diffracted light does not meet the requirements of total internal reflection due to difference in refractive indices and will be scattered into the cladding. In this meaning, the photonic crystal slab will not become equivalent to the three-dimensional photonic crystal which is constantly able to confine light in all three directions. Since a portion in which the periodicity of the refractive index distribution collapses in a light propagating direction is relevant to all optical functional element such as a bending portion of line-defect wave guide and optical resonant comprising a point defect in optical circuits, excluding linear line-defect wave guide, the fact that light will leaked into the cladding at these portions is a serious problem for forming an optical circuit.
Loss of light due to its leakage can be often reduced to some extent by elaborated design. Accordingly, it is considered that, although manufacturing of large scale optical integrated circuit is difficult, the photonic crystal slab can be used as a platform of small scale optical integrated circuit in which loss of light in wave guide is less.
Although the photonic crystal slab has a definite thickness, it can be said that the photonic crystal slab is a pseudo two-dimensional photonic crystal. Thus, the photonic crystal slab has characteristics with respect to light propagation, which are similar to those of the two-dimensional photonic crystal. One of the characteristics is mode separation of guided wave depending upon the light polarization direction.
There exist in the wave-guide mode of the two-dimensional photonic crystal and its line-defect wave guide, two modes which are independent to each other. The two modes comprises a transverse magnetic mode (TM mode) in which only magnetic field components exist in two directions parallel to a desired periodical plane and a transverse electric mode (TE mode) in which only an electric field component exists in one direction normal to the periodical plane. Since some publications define TM and TE modes, vice versa, attention should be paid to find the exact directions of electric and magnetic fields. The above-mentioned definition will be consistently adopted herein. The two wave-guide modes will not interfere and couple with each other even when light of both mode have the same frequency. Separation of the wave-guide mode into TM and TE mode is due to the fact that the distribution of the refractive index of the two-dimensional photonic crystal is uniform in a direction normal to the periodical plane, resulting in that the two-dimensional photonic crystal has a structure which is mirror symmetrical with respect to a desired periodical plane.
The photonic crystal slab and its line-defect wave guide have a refractive index distribution which is not uniform in a thicknesswise direction. If the refractive index distribution is mirror-symmetrical in a thicknesswise direction, the wave-guide mode is separated into two wave-guide modes in which the electric field is perpendicular to the magnetic field on its mirror symmetrical plane. One of two modes is a TM-like mode having properties of TM mode while the other mode is TE-like mode having properties of TE mode. Both TM- and TE-like modes will not interfere with each other for coupling even at the same frequency.
A requirement that the refractive index distribution be mirror-symmetrical in a thicknesswise direction is only requited to be substantially met in a range in which the electromagnetic energy of the wave-guided light is distributed. Since the electromagnetic energy of wave-guided light is confined in the vicinity of a core, it suffices that the refractive index distribution is mirror-symmetrical in the vicinity of a core and parts adjacent thereto of a cladding layer. Even if such a mirror-symmetrical structure is applied to the other substrate, that is, the whole of the structure does not meet the mirror-symmetry, the mirror-symmetry of the photonic crystal slab structure for guide light is not substantially lost provided that the refractive index distribution is mirror-symmetrical even in the vicinity of the core in which the light energy of wave-guided light is distributed. A term “mirror-symmetrical” will be used herein in this meaning unless otherwise defined.
The fact that the wave-guide modes of the photonic crystal slab can be separated into TM-like mode and TE-like mode is very important to use the line-defect wave guide of the photonic crystal slab. This is due to the fact that the photonic band gaps for TM-like mode and TE-like modes in the photonic crystal slab generally exists in different frequency ranges. If there is a frequency range in which the photonic band gaps of both modes overlaps, this range is limited to a narrow one. Accordingly, when the line-defect of the photonic crystal slab is used as a light wave guide by advantageously utilizing the properties of the photonic band gap, a need to use either one of TM-like mode and TE-like mode arises.
If the refractive index distribution of the photonic crystal slab becomes mirror-asymmetrical in a thicknesswise direction, two modes which are to be TM-like mode would couple with each other to become one mode. As a result, light which could have been input into the line-defect wave guide in TM-like mode will not be confined in the vicinity of the line-defect and will be leaked away.
Thus, mirror-symmetry of the refractive index distribution of the photonic crystal slab in such a manner is a requirement to separate between TM-like mode and TE-like mode.
For realizing of a photonic crystal slab having a refractive index distribution which is mirror-symmetrical, ease of manufacturing of the photonic crystal slab is an important factor. If its fabrication is difficult, the mirror-symmetry of the refractive index is critically liable to collapse. Loss of the wave-guided light may occur depending upon slight coupling between TM-like mode and TE-like mode. Therefore, a specific photonic crystal slab structure for easy fabrication is needed.
Fabrication of the photonic crystal slab having a refractive index distribution which is mirror-symmetrical in a thicknesswise direction is easy in case in which the refractive index of the medium atoms of the core is lower than that of the background medium. For simplicity of description, a crystal in which the refractive index of the medium atoms of the core is lower than that of the background will be hereinafter referred to as “hole type crystal” and below-mentioned crystal in which the refractive index of the medium atoms is higher than that of the background medium will be hereinafter referred to as “pillar-type crystal”.
A hole-type photonic crystal slab is prepared by forming a plurality of circular holes in a triangular array in a membrane made of a semiconductor having a high refractive index of 3.5, such as silicon or gallium arsenide. The membrane is suspended with ends thereof supported. In this case, the air in the holes (refractive index is 1) is the medium atom and the semiconductor constitutes the core as the background medium. The air above and below the core serves as a dielectric material which plays a role of cladding.
Fabrication process is as follows: A photo resist mask which is formed with a plurality of holes arranged in a triangular lattice array is formed on a silicon thin film formed on a silicon oxide film by using the electron beam lithography.
Then, the photo resist mask pattern is transferred to the silicon thin film by an anisotropic dry etching using a fluorine based gas.
Then, the silicon oxide film under the silicon thin film is removed by wet etching using fluoric acid.
The silicon thin film should be vertically etched. This can be comparatively easily achieved if the thickness of the silicon thin film is about 1 μm (micro meter) or less. Even if part of the silicon oxide film which is an under-layer is etched during processing of the silicon thin film, no problem will occur since all of the silicon oxide film will be removed thereafter by wet etching. In such a manner, the refractive index distribution can be easily made mirror-symmetrical in a thicknesswise direction with a high precision for the hole-type photonic crystal slab which is slab type.
In case of a pillar-type photonic crystal slab, a membrane structure which uses the air as background medium cannot be implemented, since there is no way to suspend pillars which are medium atoms of the core, in the air.
Accordingly, a membrane structure is made by using a solid dielectric medium having intensity as the background medium of the core in lieu of the air. Alternatively, in order to avoid the adoption of the membrane, it is necessary to sandwich the solid medium atoms between solid claddings. In order to fabricate the former membrane type structure, a new step to fill among the medium atoms, a dielectric material which will become a background medium is newly necessary after fabrication of the medium atoms. In order to fabricate the latter structure in which the medium atoms is sandwiched between the solid claddings, a step to form cladding layer on the core layer is necessary after the formation of the core layer.
As mentioned above, means for implementing the photonic crystal slab having its refractive distribution which is mirror-symmetrical in a thicknesswise direction has been provided in the prior art.
[Patent Document 1] Japanese Patent Kokai Publication No. JP-P2003-0043277A (FIG. 1)
[Non-Patent Document 1] Solid Physics, Vol. 32. No. 11, 1977, 862 p